Pre-coding optimization design method of MMU-MIMO-OFDM system suitable for low PAPR perception

Abstract

The invention discloses a precoding optimization design method of an MMU-MIMO-OFDM system suitable for low PAPR perception, which comprises the following steps: setting data configuration of a base station, and precoding an input symbol vector by the base station; designing the form of a precoding matrix; designing a signal of a receiver end; defining transmitting power c; according to the PAPR constraint and the MUI constraint of each antenna, establishing a PAPR sensing precoding optimization problem based on the minimization of the transmitting power c; and solving a PAPR perception precoding optimization problem by using the designed projection gradient method under the PAPR constraint and the MUI constraint of each antenna, so that the transmitting power c of all users is minimized. According to the method, the PGM-QC method is used in the optimization process, the total transmitting power c of the system is minimized only through few iterations, the complexity is greatly reduced, the operation efficiency of the system is improved, and the method is more suitable for application in engineering practice.

Description

Technical Field

[0001] The invention belongs to the field of wireless communications, and in particular relates to a precoding optimization design method suitable for a low PAPR-aware MMU-MIMO-OFDM system. Background Art

[0002] At present, massive MIMO technology is developing rapidly. As one of the important technologies in wireless communication systems, massive MIMO technology will play a very important role in the fifth generation communication system. This technology can generate a large number of spatial degrees of freedom and improve signal quality and coverage. However, in actual wireless communication, frequency selective fading is a common problem. In order to combat frequency selective fading, OFDM technology has been widely recognized. Therefore, in the next generation of communication systems, combining massive MIMO and OFDM can give full play to their respective advantages and become an indispensable core technology in the communication system. The so-called MMU-MIMO-OFDM system is that at the transmitting end, multiple data streams are transmitted on different subcarriers through multiple antennas using OFDM technology after being coded, modulated, etc.; at the receiving end, multiple antennas are used to receive signals, and each data stream is separated through signal processing algorithms, while combating the effects of multipath fading and interference in the channel. Therefore, the existence of a high PAPR in this system has become an inevitable negative impact, and thus reducing the PAPR of the system has become an issue that cannot be ignored in this system.

[0003] Existing technologies for reducing the PAPR of massive MIMO-OFDM systems, such as the fast iterative truncation algorithm, effectively solve the PAPR-aware precoding problem and reduce the PAPR of the system, but this method has extremely high computational complexity; another example is the use of an advanced Bayesian technique to solve the PAPR problem in wireless communication systems. This method specifically targets the PAPR-aware precoding problem of the system, but this method relies on several assumptions, which limits its practicality in practical applications. These methods mainly focus on solving relaxed convex optimization problems, which can only provide suboptimal solutions for the original non-convex PAPR-aware precoding. Summary of the invention

[0004] Purpose of the invention: In order to overcome the deficiencies in the prior art, a precoding optimization design method suitable for a low PAPR-aware MMU-MIMO-OFDM system is provided. In the optimization process, the PGM-QC method is used to minimize the total transmission power c of the system with only a small number of iterations, and the complexity is greatly reduced, the system operation efficiency is improved, and it is more in line with the application in actual engineering.

[0005] Technical solution: To achieve the above object, the present invention provides a precoding optimization design method for a low PAPR-aware MMU-MIMO-OFDM system, comprising the following steps:

[0006] S1: Set the base station data configuration. The base station will input the symbol vector Precoding is performed to generate a normalized precoded signal The precoding process is written as is the precoding matrix associated with the kth subcarrier;

[0007] S2: The precoding matrix is ​​designed as Among them, H k is the channel matrix associated with the kth subcarrier, used to completely eliminate the MUI matrix;

[0008] S3: Design the signal at the receiver end:

[0009] Let c i It is a time domain transmission signal. In order to eliminate inter-symbol interference, a cyclic prefix is ​​added to the time domain signal c i ; Thus, the frequency domain signal at the receiving end is obtained by removing the cyclic prefix and performing fast Fourier transform where n k ~CN(0,N 0 ), and the signal c i Typically have a higher PAPR;

[0010] S4: According to the PAPR constraint and MUI constraint of each antenna, a PAPR-aware precoding optimization problem based on minimizing the transmit power c is established;

[0011] S5: Using the designed projected gradient method, the PAPR-aware precoding optimization problem established in step S4 is solved under the PAPR constraint and MUI constraint of each antenna to minimize the transmission power c of all users.

[0012] Furthermore, in step S1, the base station is configured with M t antennas to simulate the downlink transmission of the system and provide services to U users at the same time. t >>U, In addition, it is assumed that the channel state information (CSI) of all relevant channels is completely known at the BS.

[0013] Furthermore, after precoding in step S1, the process is represented as follows: in represents the frequency domain signal to be transmitted from the ith antenna, is the mapping matrix.

[0014] Further, in step S3, Perform discrete Fourier transform to obtain the time domain signal c i ,in F JK is a JK point IDFT matrix; the time domain signal c i The PAPR is defined as:

[0015]

[0016] Furthermore, in order to perfectly eliminate MUI in step S4, the precoded signal satisfies in and is a block diagonal matrix with diagonal elements H k ,again have:

[0017]

[0018] in,

[0019] The PAPR (c i )≤β i and Under the constraints, the PAPR-aware precoding optimization problem is established:

[0020]

[0021] In order to ensure that the feasible region is not empty, let β i ≥1 and δ e ≤-60dB. β i represents the PAPR threshold that limits the output signal of each antenna, and its value is determined by the characteristics of the power amplifier, the modulation method, and the number of subcarriers; and δ e Represents the threshold for limiting the multi-user interference suffered by each antenna, and its value is determined by the system capacity and performance, the number of antennas and users, and the channel environment.

[0022] Furthermore, in step S5, the closed-form solutions of the variables c and y are solved respectively, and then the PAPR-aware precoding optimization problem is iteratively solved by adopting the projected gradient method, that is, problems (3) to (5), which specifically include:

[0023] A1: Based on the PAPR-aware precoding optimization problems (3) to (5), an optimization model is designed:

[0024] If y is set as an auxiliary variable, the optimization problems (3) to (5) are equivalent to:

[0025]

[0026] sty=s-Ac (7)

[0027]

[0028] Introducing the MUI constraint of each antenna into the objective function, the optimization problems (6) to (9) are equivalent to the following optimization:

[0029]

[0030] Where ρ>0; Assume And define Γ={c i :PAPR(c i )≤β i}, Then the iterative process of PGM-QC is as follows:

[0031]

[0032] in, is a given vector z to a set The projection on is defined as follows:

[0033]

[0034] A2: Solve subproblem (13) and obtain the closed-form solution of c;

[0035] A3: Solve subproblem (14) and obtain the optimal solution for y.

[0036] Furthermore, the step A2 specifically includes:

[0037] Assumptions Then subproblem (13) is equivalent to the following optimization problem:

[0038]

[0039] in, The optimization problems (16) to (17) are decomposed into M t Sub-questions:

[0040]

[0041] stPAPR(c i )≤β i (19)

[0042] Let ci =t i d i ,t i >0 and And bring it into the above optimization to get the following optimization problem:

[0043]

[0044]

[0045] In order to minimize the objective function (20) in the above optimization, we maximize And replace constraint (22) with an inequality constraint to produce an equivalent convex optimization problem:

[0046]

[0047] In order to obtain a more efficient solution, formula (25) is added to formula (23) as a penalty term, which forms the following optimization problem:

[0048]

[0049] where α n >0 is the penalty parameter, '*' is the conjugate operator; the above optimization is decomposed into JK sub-problems, which means that the above problem is transformed into solving JK parallel sub-problems:

[0050]

[0051] Deriving the objective function and setting it to 0, projecting the solution onto the feasible domain, we obtain the following closed-form solution:

[0052]

[0053] In addition, the penalty term α is solved by the binary method, and then d i Substitute into formula (20) to (22) and simplify to obtain t i The closed-form solution of is:

[0054]

[0055] Apparently It always holds true; therefore, the closed-form solution of c is obtained through parallel computing as follows:

[0056]

[0057] Furthermore, the step A3 specifically includes:

[0058] Assumptions Then subproblem (14) is equivalent to the following optimization problem:

[0059] min||yv n || 2 (33)

[0060] st‖y‖ 2 ≤δ e (34)

[0061] Then the optimal solution for y is given by:

[0062]

[0063] Furthermore, the process of solving the penalty term α using the dichotomy method in step A2 is:

[0064] B1: Initialization:

[0065] Setting Boundaries set up and Large enough;

[0066] B2: Solve for α:

[0067] make Calculated by formula (30) And prepare for subsequent solutions;

[0068] when Sometimes, there is otherwise until When

[0069] The solution obtained in this way avoids the problem of excessive complexity. Although it is an approximate method, the expected effect can be achieved by flexibly adjusting the sizes of the two parameters.

[0070] Furthermore, solving problem (3) in step S5 includes the following steps:

[0071] C1: Input: s, A, μ, ρ>0;

[0072] C2: Initialization: c 0 ,y 0 ;

[0073] C3: When not converged, execute M t parallel computing:

[0074] Update:d i

[0075] Update: i

[0076] Update: c i

[0077] End parallel computing

[0078] C4: Update: y

[0079] C5: Output: c.

[0080] The present invention proposes a PGM-QC method to solve the relaxed convex optimization problem. In a large-scale MU-MIMO-OFDM downlink system, this method utilizes the rich degrees of freedom brought by the large-scale antenna array configured on the base station. This method constructs a non-convex optimization problem including OFDM modulation, multi-user precoding, MUI and PAPR constraints to minimize the total transmission power of the system. Different from the existing methods, this method uses the projected gradient descent algorithm developed on the basis of the PGM algorithm to solve this non-convex PAPR-aware precoding problem. Each sub-problem of this method has a simple closed-form solution, thereby avoiding the inverse operation of the high-dimensional matrix, thereby reducing the computational complexity, and the PAPR of the optimized signal is approximately constant and has a lower MUI.

[0081] For the next generation of communication technology, the MMU-MIMO-OFDM system will inevitably become an indispensable core technology. The low PAPR-aware MMU-MIMO-OFDM system will become the key technology of the next generation of communication technology with its low PAPR, low MUI and high stability.

[0082] The present invention studies the massive multi-user multiple input multiple output orthogonal frequency division multiplexing (MMU-MIMO-OFDM) downlink system, and solves the problem of minimizing the transmission power by solving the condition that the peak-to-average ratio (PAPR) and multi-user interference (MUI) on each antenna are lower than the predetermined threshold through the rich degrees of freedom provided by the massive antenna array equipped on the base station. Considering that this is a non-convex optimization problem, the projected gradient descent method (PGM) is used to solve the non-convex PAPR-aware precoding optimization problem, which has excellent performance in reducing the PAPR of the system and minimizing the symbol error rate (SER).

[0083] Beneficial effects: Compared with the prior art, the present invention proposes a low-complexity PGM-QC method for reducing the PAPR problem of the MMU-MIMO-OFDM system. The core is to find a simple closed-form solution for each sub-problem, which minimizes the total transmission power of the system. In addition, the use of the PGM-QC method in the optimization process only requires low computational complexity to minimize the total transmission power of the system, thereby improving the efficiency of the system and making it more suitable for practical engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] Figure 1 This is a block diagram of the downlink of a massive MU-MIMO-OFDM system;

[0085] Figure 2 It is the convergence diagram of PGM-QC algorithm;

[0086] Figure 3 This is a comparison chart of PAPR performance of different methods;

[0087] Figure 4 This is a comparison chart of SER performance of different methods. DETAILED DESCRIPTION

[0088] The present invention is further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent forms of modifications to the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0089] Embodiment 1:

[0090] This embodiment provides a precoding optimization design method for a low PAPR-aware MMU-MIMO-OFDM system. Figure 1 , which comprises the following steps:

[0091] S1: Set the base station data configuration. The base station will input the symbol vector Precoding is performed to generate a normalized precoded signal The precoding process is written as is the precoding matrix associated with the kth subcarrier;

[0092] Set up base station configuration t antennas to simulate the downlink transmission of the system and provide services to U users at the same time. t >>U, In addition, it is assumed that the channel state information (CSI) of all relevant channels is completely known at the BS.

[0093] After precoding, it is expressed as the following process: in represents the frequency domain signal to be transmitted from the ith antenna, is the mapping matrix.

[0094] S2: The precoding matrix is ​​designed as Among them, H k is the channel matrix associated with the kth subcarrier, used to completely eliminate the MUI matrix;

[0095] It should be noted here that: after the information sent to the user is pre-coded, the information received at the receiving end is y = HH H s+n, where n is the noise vector. Since HH H =I U Therefore, the above formula can be transformed into U independent single-stream systems y=s+n. At this time, since the information of different users is independent of each other at the receiving end, the interference between multiple users is eliminated, that is, MUI is eliminated.

[0096] S3: Design the signal at the receiver end:

[0097] Let c i It is a time domain transmission signal. In order to eliminate inter-symbol interference, a cyclic prefix is ​​added to the time domain signal c i ; Thus, the frequency domain signal at the receiving end is obtained by removing the cyclic prefix and performing fast Fourier transform where n k ~CN(0,N 0 ), and the signal c i Usually have a higher PAPP;

[0098] Through Perform discrete Fourier transform to obtain the time domain signal c i ,in F JK is a JK point IDFT matrix; the time domain signal c i The PAPR is defined as:

[0099]

[0100] S4: According to the PAPR constraint and MUI constraint of each antenna, a PAPR-aware precoding optimization problem based on minimizing the transmit power c is established;

[0101] In order to perfectly eliminate MUI, the precoded signal meets in and is a block diagonal matrix with diagonal elements H k ,again have:

[0102]

[0103] in,

[0104] The PAPR (c i )≤β i and Under the constraints, the PAPR-aware precoding optimization problem is established:

[0105]

[0106] In order to ensure that the feasible region is not empty, let β i ≥1 and δ e ≤-60dB. Among them, β i represents the PAPR threshold that limits the output signal of each antenna, and its value is determined by the characteristics of the power amplifier, the modulation method, and the number of subcarriers; and δ e Represents the threshold for limiting the multi-user interference suffered by each antenna, and its value is determined by the system capacity and performance, the number of antennas and users, and the channel environment.

[0107] S5: Using the designed projected gradient method, under the PAPR constraint and MUI constraint of each antenna, solve the PAPR-aware precoding optimization problem established in step S4 to minimize the transmit power c of all users;

[0108] Step S5 will solve the closed-form solutions of variables c and y respectively, and then iteratively solve the PAPR-aware precoding optimization problem by adopting the projected gradient method, that is, problems (3) to (5), which specifically include:

[0109] A1: Based on the PAPR-aware precoding optimization problems (3) to (5), an optimization model is designed:

[0110] If y is set as an auxiliary variable, the optimization problems (3) to (5) are equivalent to:

[0111]

[0112] sty=s-Ac (7)

[0113]

[0114] Introducing the MUI constraint of each antenna into the objective function, the optimization problems (6) to (9) are equivalent to the following optimization:

[0115]

[0116] Where ρ>0; Assume And define Γ={c i :PAPR(c i )≤β i}, Then the iterative process of PGM-QC is as follows:

[0117]

[0118] in, is a given vector z to a set The projection on is defined as follows:

[0119]

[0120] A2: Solve subproblem (13) and obtain the closed-form solution of c:

[0121] Assumptions Then subproblem (13) is equivalent to the following optimization problem:

[0122]

[0123] in, The optimization problems (16) to (17) are decomposed into M t Sub-questions:

[0124]

[0125] stPAPR(c i )≤β i (19)

[0126] Let c i =t i d i ,t i >0 and And bring it into the above optimization to get the following optimization problem:

[0127]

[0128] In order to minimize the objective function (20) in the above optimization, we maximize And replace constraint (22) with an inequality constraint to produce an equivalent convex optimization problem:

[0129]

[0130]

[0131] In order to obtain a more efficient solution, formula (25) is added to formula (23) as a penalty term, which forms the following optimization problem:

[0132]

[0133] where α n >0 is the penalty parameter, '*' is the conjugate operator; the above optimization is decomposed into JK sub-problems, which means that the above problem is transformed into solving JK parallel sub-problems:

[0134]

[0135] Deriving the objective function and setting it to 0, projecting the solution onto the feasible domain, we obtain the following closed-form solution:

[0136]

[0137] In addition, the penalty term α is solved by the binary method, and then d i Substitute into formula (20) to (22) and simplify to obtain t i The closed-form solution of is:

[0138]

[0139] Apparently It always holds true; therefore, the closed-form solution of c is obtained through parallel computing as follows:

[0140]

[0141] A3: Solve subproblem (14) and obtain the optimal solution for y:

[0142] Assumptions Then subproblem (14) is equivalent to the following optimization problem:

[0143]

[0144] st||y|| 2 ≤δ e (34)

[0145] Then the optimal solution for y is given by:

[0146]

[0147] The process of using the dichotomy method to solve the penalty term α in step A2 is:

[0148] B1: Initialization:

[0149] Setting Boundaries set up and Large enough ( Set it to be large enough. There is no specific standard for this large enough, and it generally depends on the actual situation of the problem);

[0150] B2: Solve for α:

[0151] make Calculated by formula (30) And prepare for subsequent solutions;

[0152] when Sometimes, there is otherwise until When

[0153] The solution obtained in this way avoids the problem of excessive complexity. Although it is an approximate method, the expected effect can be achieved by flexibly adjusting the sizes of the two parameters (μ and ρ in step C1).

[0154] Therefore, solving problem (3) in step S5 includes the following steps:

[0155] C1: Input: s, A, μ, ρ>0;

[0156] C2: Initialization: c 0 ,y 0 ;

[0157] C3: When not converged, execute M t parallel computing:

[0158] Update:d i

[0159] Update: i

[0160] Update: c i

[0161] End parallel computing

[0162] C4: Update: y

[0163] C5: Output: c.

[0164] Embodiment 2:

[0165] This embodiment provides a precoding optimization design system suitable for a low PAPR-aware MMU-MIMO-OFDM system, the system comprising a network interface, a memory and a processor; wherein the network interface is used to realize the reception and transmission of signals during the process of sending and receiving information between other external network elements; the memory is used to store computer program instructions that can be run on the processor; the processor is used to execute the steps of the above-mentioned consensus method when running the computer program instructions.

[0166] The present embodiment also provides a computer storage medium, which stores a computer program, and the method described above can be implemented when the processor executes the computer program. The computer readable medium can be considered to be tangible and non-temporary. Non-limiting examples of non-temporary tangible computer-readable media include non-volatile memory circuits (such as flash memory circuits, erasable programmable read-only memory circuits or mask read-only memory circuits), volatile memory circuits (such as static random access memory circuits or dynamic random access memory circuits), magnetic storage media (such as analog or digital tapes or hard drives) and optical storage media (such as CDs, DVDs or Blu-ray discs), etc. The computer program includes processor executable instructions stored on at least one non-temporary tangible computer-readable medium. The computer program may also include or rely on stored data. The computer program may include a basic input / output system (BIOS) that interacts with the hardware of a special-purpose computer, a device driver that interacts with a specific device of a special-purpose computer, one or more operating systems, user applications, background services, background applications, etc.

[0167] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0168] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0169] Embodiment 3:

[0170] Based on the solutions provided in Examples 1 and 2, in order to verify the effect of the method of the present invention, this embodiment conducts a simulation experiment of the algorithm, uses the software MATLAB to perform simulation, and verifies the theoretical analysis. The specific simulation results and analysis are as follows:

[0171] like Figure 2 The figure shows the convergence diagram of the PGM-QC algorithm. In this embodiment, the termination condition of the PGM-QC algorithm is set to ε≤10 -6 , which is sufficient for practical applications. At about 50 iterations, ε is 10 -4 As the number of iterations increases, when the number of iterations is 200, ε is approximately 10 -6 Although the residual error fluctuates between the 200th and 400th iterations, the fluctuation range is small, which indicates that the algorithm is converged.

[0172] like Figure 3 The figure shows the PAPR performance of different algorithms. This figure plots the complementary cumulative distribution function (CCDF) curves of various algorithms under convergence conditions. The definition of CCDF is given by the probability that the PAPR of the MIMO-OFDM signal exceeds the threshold, that is, CCDF = Pr (PAPR>ψ). It can be seen from the figure that the PAPR of the PGM-QC algorithm is much better than that of other algorithms, and the PGM-QC algorithm has a CCDF curve with a cutoff, while other algorithms do not. This phenomenon shows that other algorithms still have a large PAPR.

[0173] like Figure 4 The figure shows the SER performance comparison of different methods, which describes the signal-to-noise ratio performance of different methods after the solid-state power amplifier (SSPA) input power is reduced by 3dB. It can be seen from the figure that when SNR=10 -3 When compared with the ideal linear ZF precoding, the signal-to-noise ratio performance loss of the PGM-QC algorithm is about 1.1dB, which is much better than other algorithms.

[0174] It can be seen from the above simulation experiments that the PGM-QC algorithm has lower complexity and better performance. Therefore, the PGM-QC method provided by the present invention is more efficient than other methods and is more conducive to application in engineering practice.

Claims

1. A precoding optimization design method for a low PAPR-aware MMU-MIMO-OFDM system, characterized in that: The steps include: S1: Set the base station data configuration. The base station will input the symbol vector Precoding is performed to generate a normalized precoded signal The precoding process is written as is the precoding matrix associated with the kth subcarrier; S2: The precoding matrix is ​​designed as Among them, H k is the channel matrix associated with the kth subcarrier, used to completely eliminate the MUI matrix; S3: Design the signal at the receiver end: Let c i It is a time domain transmission signal. In order to eliminate inter-symbol interference, a cyclic prefix is ​​added to the time domain signal c i ; Thus, the frequency domain signal at the receiving end is obtained by removing the cyclic prefix and performing fast Fourier transform Where n k ~CN(0,N0); S4: According to the PAPR constraint and MUI constraint of each antenna, a PAPR-aware precoding optimization problem based on minimizing the transmit power c is established; S5: Using the designed projected gradient method, the PAPR-aware precoding optimization problem established in step S4 is solved under the PAPR constraint and MUI constraint of each antenna to minimize the transmission power c of all users.

2. The precoding optimization design method for a low PAPR-aware MMU-MIMO-OFDM system according to claim 1, characterized in that: In step S1, the base station configuration M is set t antennas to simulate the downlink transmission of the system and provide services to U users at the same time. t >>U.

3. The precoding optimization design method for a low PAPR-aware MMU-MIMO-OFDM system according to claim 2, characterized in that: After precoding in step S1, the process is represented as follows: in represents the frequency domain signal to be transmitted from the ith antenna, is the mapping matrix.

4. The precoding optimization design method for a low PAPR-aware MMU-MIMO-OFDM system according to claim 3, characterized in that: In step S3, Perform discrete Fourier transform to obtain the time domain signal c i ,in F JK is a JK point IDFT matrix; the time domain signal c i The PAPR is defined as:

5. The precoding optimization design method for a low PAPR-aware MMU-MIMO-OFDM system according to claim 4, characterized in that: In step S4, the precoded signal satisfies in and is a block diagonal matrix with diagonal elements H k ,again have: in, The PAPR (c i )≤β i and Under the constraints, the PAPR-aware precoding optimization problem is established: Among them, β i Represents the PAPR threshold that limits the output signal of each antenna; δ e Represents the threshold that limits the multi-user interference experienced by each antenna.

6. The precoding optimization design method for a low PAPR-aware MMU-MIMO-OFDM system according to claim 5, characterized in that: The step S5 specifically includes: A1: Based on the PAPR-aware precoding optimization problems (3) to (5), an optimization model is designed: If y is set as an auxiliary variable, the optimization problems (3) to (5) are equivalent to: sty=s-Ac (7) Introducing the MUI constraint of each antenna into the objective function, the optimization problems (6) to (9) are equivalent to the following optimization: Where ρ>0; Assume And define Γ={c i :PAPR(c i )≤β i }, Then the iterative process of PGM-QC is as follows: in, is a given vector z to a set The projection onto is defined as follows: A2: Solve subproblem (13) and obtain the closed-form solution of c; A3: Solve subproblem (14) and obtain the optimal solution for y.

7. The precoding optimization design method for a low PAPR-aware MMU-MIMO-OFDM system according to claim 6, characterized in that: The step A2 specifically includes: Assumptions Then subproblem (13) is equivalent to the following optimization problem: in, The optimization problems (16) to (17) are decomposed into M t Sub-questions: s.t.PAPR(c i )≤β i (19) Let c i =t i d i ,t i >0 and And bring it into the above optimization to get the following optimization problem: In order to minimize the objective function (20) in the above optimization, we maximize And replace constraint (22) with an inequality constraint to produce an equivalent convex optimization problem: Adding formula (25) as a penalty term to formula (23) forms the following optimization problem: where α n >0 is the penalty parameter, '*' is the conjugate operator; the above optimization is decomposed into JK sub-problems, and the above problem is transformed into solving JK parallel sub-problems: Deriving the objective function and setting it to 0, projecting the solution onto the feasible domain, we obtain the following closed-form solution: Solve the penalty term α by binary search, and then i Substituting into formulas (20) to (22) and simplifying, we can obtain the closed-form solution of ti: Apparently It always holds true; therefore, the closed-form solution of c is obtained through parallel computing as follows:

8. The precoding optimization design method for a low PAPR-aware MMU-MIMO-OFDM system according to claim 7, characterized in that: The step A3 specifically includes: Assumptions Then subproblem (14) is equivalent to the following optimization problem: min||yv n || 2 (33) s.t.||y|| 2 ≤δ e (34) Then the optimal solution for y is given by:

9. The precoding optimization design method for a low PAPR-aware MMU-MIMO-OFDM system according to claim 7, characterized in that: The process of using the dichotomy method to solve the penalty term α in step A2 is: B1: Initialization: Setting Boundaries set up and Large enough; B2: Solve for α: make Calculated by formula (30) And prepare for subsequent solutions; when Sometimes, there are otherwise until When 10. The precoding optimization design method for a low PAPR-aware MMU-MIMO-OFDM system according to claim 7, characterized in that: Solving problem (3) in step S5 includes the following steps: C1: Input: s, A, μ, ρ>0; C2: Initialization: c 0 ,y 0 ; C3: When not converged, execute M t parallel computing: Update: d i Update: i Update: c i End parallel computing C4: Update: y C5: Output: c.

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